Solve for the slope of the following equations:?

Question

1. f(x)=3x+5=7
2. f(x)= 3/2x-4=5
3. f(x)=5x-7
4. f(x)= -4/5x+4

Answer 1

All of them are of the form y = mx + c and here we have for example,

f(x) = -4/5x + 4

Substitute y for f(x) and you will see that m = -4/5

Similarly you can find out the slope of others too.

Answer 2

To find the slope derive f:

1. f'(x)=3 at every point.

2. f'(x) = -2*3/(2x)^2 = -2*3/(4x^2) = -3/(2x^2)

Where f(x)=5

3/2x-4=5 -> 3/2x=9 -> 1/x = 9*2/3=6 ->
-3/(2x^2) = -3/2x * 1/x = -9*6 = -54

3. f'(x)=5 everywhere.

4. f'(x) = 5*4/(5x)^2 = 5*4/(5*5*x^2) = 4/(5x^2)